Henning, as the others have mentioned, the running water isn't a problem. The heat of mixing is really only a big deal when you add water slowly to acid -- if you quickly flood the container with water, the exotherm won't be a big problem. (Don't splash it in your eyes!)
I agree with avandesande that the best thing is to imagine anything that could go wrong, and to prepare ahead for it (make a plan)... and that lithium amide story is pretty sad. I can't imagine working with it on a plant scale. A few grams at a time is fine.
Once I was doing a trans-metalation reaction at -78C using tert-butyllithium. It ended up precipitating during the addition, and the re-dissolution as the reaction warmed up was VERY EXOTHERMIC... not a pretty sight.
Don't be too scared of sulfuric acid -- use your head and you'll be fine -- but if you can find "pH Minus" or another swimming-pool-supply source of sodium bisulfate, it'll be much more convenient.